DiNardo-Fortin-Lemieux reweighting: composition and structure without a linear model

Group 0 is reweighted by \(\psi(x) = m_1(x)/m_0(x)\), the ratio of the two groups' masses at each covariate value. The reweighted group has group 1's covariate distribution exactly (Research.P15Reweight.reweighting_matches, reweighted_mass), so its outcome mean is the counterfactual "group 1's composition at group 0's structure" (counterfactual_outcome), and the raw gap splits into structure \(m_1 - m_{cf}\) and composition \(m_{cf} - m_0\) (decomposition). Common support is required: a covariate value present in group 1 but absent from group 0 is an error.

Usage

morie_dfl_reweight(group, x, y, weights = NULL)

Arguments

group: Logical or 0/1: TRUE for group 1 (whose composition is imposed), FALSE for group 0 (reweighted).
x: Discrete covariate (a vector; combine several with interaction()).
y: Outcome.
weights: Optional non-negative weights.

Value

A list with mean_1, mean_0, counterfactual, structure, composition, psi (a data frame with x, mass_1, mass_0, psi), max_composition_gap (largest difference between the reweighted and group-1 covariate shares; zero by the theorem) and theorems.

Examples

g <- c(rep(TRUE, 6), rep(FALSE, 6))
x <- c("a", "a", "a", "a", "b", "b",  "a", "a", "b", "b", "b", "b")
y <- c(10, 12, 11, 13, 20, 22,  8, 9, 15, 16, 14, 17)
r <- morie_dfl_reweight(g, x, y)
c(mean_1 = r$mean_1, mean_0 = r$mean_0, cf = r$counterfactual, structure = r$structure, composition = r$composition)
#>      mean_1      mean_0          cf   structure composition 
#>   14.666667   13.166667   10.833333    3.833333   -2.333333